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Apple·Software Engineer·Technical Phone Screen·Senior

Senior
May 2026

Summary

Apple SWE interview with a greedy algorithm problem that looks deceptively clean on paper but has a lot of moving parts when you actually try to implement it efficiently. One question, but it had multiple layers they kept pushing on.

Questions Asked (1)

Q1

You start with some initial capital W and can complete at most K projects. Each project has a minimum capital requirement and a profit value. You can only start a project if your current funds meet its requirement, and completing it adds the profit to your funds. Design an efficient algorithm to maximize your final capital, including data structure choices, time and space complexity analysis, correctness justification, and how it scales to N around 200,000.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

I got the greedy intuition pretty fast: always pick the highest-profit available project.

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AI HintsAI Generated

Suggested Approach

Start by restating the problem and clarifying constraints, then propose a greedy strategy using a min-heap to always select the most profitable project among those currently affordable. Walk through the algorithm step-by-step, analyze time and space complexity, and justify correctness with an exchange argument. Finally, discuss how the approach scales to N=200,000 and mention potential optimizations.

Pro tip: Emphasize that the greedy choice is safe because profits are positive and selecting the highest profit affordable project never reduces future affordability. Also, mention that sorting projects by capital requirement and using a min-heap for profits is a classic pattern for this type of problem.

1. Understand and Restate the Problem

Confirm the inputs (initial capital W, max projects K, arrays of capital requirements and profits) and the goal (maximize final capital). Clarify that you can complete at most K projects, not exactly K, and that projects can be done in any order as long as capital requirements are met.

2. Design the Greedy Algorithm

Sort projects by capital requirement. Use a min-heap to store profits of projects that are currently affordable. At each step, add all projects with requirement ≤ current capital to the heap, then if heap is non-empty and we haven't done K projects, pop the max profit (simulate by using a max-heap or negating values) and add it to capital.

3. Analyze Complexity and Correctness

Time complexity: O(N log N) due to sorting and heap operations. Space complexity: O(N) for the heap and sorted list. Correctness: prove by exchange argument that selecting the highest profit affordable project at each step leads to an optimal solution.

4. Discuss Scalability and Edge Cases

Explain that O(N log N) is efficient for N=200,000. Mention edge cases: no affordable projects, K=0, all projects affordable initially, and projects with zero profit. Also, note that if K is large, the algorithm naturally stops when no more projects can be done.

Key Points to Mention

  • Greedy strategy: always pick the most profitable project among those currently affordable.
  • Use a min-heap (or max-heap) to efficiently retrieve the maximum profit.
  • Sort projects by capital requirement to process them in order of affordability.
  • Time complexity: O(N log N) due to sorting and heap operations; space complexity: O(N).
  • Correctness proof via exchange argument: swapping a chosen project with a higher-profit affordable one never hurts.
  • Scalability: handles N=200,000 within typical time limits; can be optimized by early termination when no projects are affordable or K projects are done.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.